Motoko Kusanagi - Ghost in the shell
Casca - Berserk
Most of the female cast of Evangelion
There are others but the names currently escape me and I'm at work without enough time to go look them up.
OH! Most of the Mobile Suit Gundam female cast before 1998.

I think the female characters of Hanasaku Iroha and Tari Tari were relatively normal...aside from particular character quirks. Their characters had solid development, and they weren't in any way overtly sexualized.

Nobody's said this that I've seen, it's a little older show but I think she fits the criteria; Kiyone from Tenchi Universe. In a show about a bunch of women slutting out for a socially retarded teenage boy, Kiyone shows no interest in anyone romantically, she's smart though completely unsuccessful as a cop due to her partner, she's (relatively) normal as far as her figure goes, she's not one of those PMS anime stereotypes that's just mad and bitchy all the time, and though she's a smaller part than the other characters she's still fairly important to the storyline and is in most episodes.

- Nanami Takahashi from Bokura Ga Ita seemed the most normal to me.
- Akashi from Tatami Galaxy also a solid choice.
- Both girls from Hyouka seem very pretty realistic (almost in a sad way for Chitanda).

- As other's have posted, Sumida from 5cm per second and Mokoto from The Girl Who Leapt Through Time

She is often the one making fun of Ash, rather then being the focus of ridicule....isn't sexualized (maybe because she should appear like a 10-13 year old?) and has her own agenda. Didn't want all too much Pokemon (<--anyone believe this?), but from what I got...she had her own issues to deal with (her gym leader sisters and the fact that Ash owed her a new bicycle).

This highly depends on the very personal definition of normal. And thats hard. Have you ever tried determinating the most normal among your friends? It's really hard, and thats in a enviornment normal by definition. Putting Anime in the mix makes things not even harder due to an increase of interesting characters in fictional works (kind of by definition), but also by diffusiong the meaning of "normal". You might take into consideration different drawing styles and different worlds (were things thoroughly abnormal are considered normal), or you might not. You might have your focus on either mind or body and how well the mind functions in the world it is set in compared to how much the mind would fit our world. And after all of that, it's still not only a matter of your own opinion but also depends on the minds of your peers on which you might base your definition of normal.

Also anime aimed at children is often guilty of stereotyping, giving figures more of a standart role than a distinctive character. And those stereotypes, although based on easy to understand and relateable traits, are far from normal as they are too basic. I only bring this up because the older seasons of Digimon were mentioned which are especially guilty of that.

And last, the amount of screentime a person gets is most likely effecting the amount of "normalness" in a negative way. Having more opportunity to act abnormal amounts to more abnormal acting.

That said, the most normal female figure of anime is probably a side figure of a hyper-realistic seinen anime we won't get fansubbed because wests interest in this is too low. Discounting several of theese aspects, I would go with Sakura from Naruto, as have others before me. But yet again, she is so "normal" in an absolutly crazy world, I feel sometimes she is the odd one.